The developmental relations between conceptual and procedural knowledge: a multimethod approach.

Interactions between conceptual and procedural knowledge influence the development of mathematical competencies. However, after decades of research, these interrelations are still under debate, and empirical results are inconclusive. The authors point out a source of these problems. Different kinds of knowledge and competencies only show up intertwined in behavior, making it hard to measure them validly and independently of each other. A multimethod approach was used to investigate the extent of these problems. A total of 289 fifth and sixth graders' conceptual and procedural knowledge about decimal fractions was measured by 4 common hypothetical measures of each kind of knowledge. Study 1 tested whether treatments affected the 2 groups of measures in consistent ways. Study 2 assessed, across 3 measurement points, whether conceptual and procedural knowledge could be modeled as latent factors underlying the measures. The results reveal substantial problems with the validities of the measures, which might have been present but gone undetected in previous studies. A solution to these problems is essential for theoretical and practical progress in the field. The potential of the multimethod approach for this enterprise is discussed.